Open Access
2011 Parameters estimation for asymmetric bifurcating autoregressive processes with missing data
Benoîte de Saporta, Anne Gégout-Petit, Laurence Marsalle
Electron. J. Statist. 5: 1313-1353 (2011). DOI: 10.1214/11-EJS643


We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the strong consistency of our estimators on the set of non-extinction of the Galton-Watson process, via a martingale approach. We also prove a quadratic strong law and the asymptotic normality.


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Benoîte de Saporta. Anne Gégout-Petit. Laurence Marsalle. "Parameters estimation for asymmetric bifurcating autoregressive processes with missing data." Electron. J. Statist. 5 1313 - 1353, 2011.


Published: 2011
First available in Project Euclid: 19 October 2011

zbMATH: 1274.62192
MathSciNet: MR2842907
Digital Object Identifier: 10.1214/11-EJS643

Primary: 62F12 , 62M09
Secondary: 60G42 , 60J80 , 92D25

Keywords: Bifurcating autoregressive process , Galton-Watson process , joint model , Least squares estimation , limit theorems , Martingales , missing data

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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